%matplotlib inline
%config InlineBackend.figure_format='retina'
from IPython.display import display, display_markdown
import warnings
warnings.simplefilter(action='ignore', category=FutureWarning)
import subprocess as sp
import numpy as np
import pandas as pd
import seaborn as sns
import arviz as az
import bambi
from copy import deepcopy
from scipy.stats import pearsonr, spearmanr
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = [10, 8]
plt.rcParams['figure.dpi'] = 150
from subs2vec.utensils import log_timer
from subs2vec.vecs import Vectors
from subs2vec.neighbors import compute_nn
import logging
logging.getLogger().setLevel(logging.WARNING)
def display_md(md, **kwargs):
return display_markdown(md, raw=True, **kwargs)
def convert_notebook(title, output='html'):
convert = sp.run(f'jupyter nbconvert {title}.ipynb --to {output} --output {title}.{output}'.split(' '))
if convert.returncode == 0:
display_md(f'Jupyter notebook `{title}` converted successfully.')
else:
display_md(f'Error: encountered problem converting Jupyter notebook `{title}`')
def norm(x):
return x / np.linalg.norm(x, 2)
def standardize(x):
return (x - x.mean()) / x.std()
sns.set(style='whitegrid')
pd.options.mode.chained_assignment = None
df_joint = pd.read_csv('data/data_plus_predictors.tsv', sep='\t')
df_joint = df_joint[df_joint['dimension'] != 'high-low']
display(df_joint)
| index | group | dimension | pp_id | color | rating | experiment | self_vs_other | art | fiction | ... | sighted | group_eff | group_z | original | replication_1 | replication_2 | other | self | self_vs_other_eff | self_vs_other_z | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | sighted | cold-hot | sighted_1 | white | 1 | original | self | NaN | NaN | ... | 1 | 1.0 | 0.211241 | 1 | 0 | 0 | 0 | 1 | -1.0 | -0.891882 |
| 1 | 1 | sighted | ripe-unripe | sighted_1 | white | 7 | original | self | NaN | NaN | ... | 1 | 1.0 | 0.211241 | 1 | 0 | 0 | 0 | 1 | -1.0 | -0.891882 |
| 2 | 2 | sighted | new-old | sighted_1 | white | 1 | original | self | NaN | NaN | ... | 1 | 1.0 | 0.211241 | 1 | 0 | 0 | 0 | 1 | -1.0 | -0.891882 |
| 3 | 3 | sighted | submissive-aggressive | sighted_1 | white | 1 | original | self | NaN | NaN | ... | 1 | 1.0 | 0.211241 | 1 | 0 | 0 | 0 | 1 | -1.0 | -0.891882 |
| 4 | 4 | sighted | selfless-jealous | sighted_1 | white | 1 | original | self | NaN | NaN | ... | 1 | 1.0 | 0.211241 | 1 | 0 | 0 | 0 | 1 | -1.0 | -0.891882 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 42974 | 28506 | sighted | soft-hard | sighted_68129 | red | 5 | replication_2 | other | 11.0 | 0.0 | ... | 1 | 1.0 | 0.211241 | 0 | 0 | 1 | 1 | 0 | 1.0 | 1.121199 |
| 42975 | 28507 | sighted | light-heavy | sighted_68129 | red | 5 | replication_2 | other | 11.0 | 0.0 | ... | 1 | 1.0 | 0.211241 | 0 | 0 | 1 | 1 | 0 | 1.0 | 1.121199 |
| 42976 | 28508 | sighted | relaxed-tense | sighted_68129 | red | 5 | replication_2 | other | 11.0 | 0.0 | ... | 1 | 1.0 | 0.211241 | 0 | 0 | 1 | 1 | 0 | 1.0 | 1.121199 |
| 42977 | 28509 | sighted | alive-dead | sighted_68129 | red | 6 | replication_2 | other | 11.0 | 0.0 | ... | 1 | 1.0 | 0.211241 | 0 | 0 | 1 | 1 | 0 | 1.0 | 1.121199 |
| 42978 | 28510 | sighted | fast-slow | sighted_68129 | red | 3 | replication_2 | other | 11.0 | 0.0 | ... | 1 | 1.0 | 0.211241 | 0 | 0 | 1 | 1 | 0 | 1.0 | 1.121199 |
40866 rows × 76 columns
replication = df_joint[df_joint['experiment'] == 'replication_1'].groupby(['dimension', 'color']).mean()
original = df_joint[(df_joint['experiment'] == 'original') & (df_joint['group'] == 'sighted')].groupby(['dimension', 'color']).mean()
r = pearsonr(replication['rating'], original['rating'])
print(f'r(original, replication) = {r[0]:.2f}, p = {r[1]:.3f}')
r = spearmanr(replication['rating'], original['rating'])
print(f'rank r(original, replication) = {r[0]:.2f}, p = {r[1]:.3f}')
r(original, replication) = 0.89, p = 0.000 rank r(original, replication) = 0.87, p = 0.000
blind = df_joint[df_joint['group'] == 'blind'].groupby(['dimension', 'color']).mean()
sighted = df_joint[((df_joint['experiment'] == 'original') | (df_joint['experiment'] == 'replication_1'))
& (df_joint['group'] == 'sighted')].groupby(['dimension', 'color']).mean()
r = pearsonr(blind['rating'], sighted['rating'])
print(f'r(blind, sighted) = {r[0]:.2f}, p = {r[1]:.3f}')
r = spearmanr(blind['rating'], sighted['rating'])
print(f'rank r(blind, sighted) = {r[0]:.2f}, p = {r[1]:.3f}')
r(blind, sighted) = 0.75, p = 0.000 rank r(blind, sighted) = 0.72, p = 0.000
m_cc = bambi.Model('rating_z ~ 1'
+ ' + group_eff*frequency_z'
+ ' + group_eff*concreteness_z'
+ ' + group_eff*cosine_cc_z'
+ ' + group_eff*swow_all_z'
+ ' + (1 + frequency_z + concreteness_z + cosine_cc_z + swow_all_z|pp_id)'
+ ' + (1 + group_eff|dimension)'
+ ' + (1 + group_eff|color)',
df_joint[(df_joint['experiment'] != 'replication_2') & (df_joint['self_vs_other'] == 'self')]
)
r_cc = m_cc.fit(
init='advi+adapt_diag',
chains=4,
draws=1000,
tune=1000,
n_init=10000,
target_accept=.95,
)
Auto-assigning NUTS sampler... [INFO] Auto-assigning NUTS sampler... Initializing NUTS using advi+adapt_diag... [INFO] Initializing NUTS using advi+adapt_diag...
Finished [100%]: Average Loss = 16,659 [INFO] Finished [100%]: Average Loss = 16,659 Multiprocess sampling (4 chains in 4 jobs) [INFO] Multiprocess sampling (4 chains in 4 jobs) NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_cc_z, group_eff:cosine_cc_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_cc_z|pp_id_sigma, cosine_cc_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma] [INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_cc_z, group_eff:cosine_cc_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_cc_z|pp_id_sigma, cosine_cc_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 387 seconds. [INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 387 seconds.
# compute and plot conditional effect of cosine in sighted and blind groups
trace = deepcopy(r_cc.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_cc_z'] = trace['cosine_cc_z'] - trace['group_eff:cosine_cc_z']
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_cc_z'] = trace['cosine_cc_z'] + trace['group_eff:cosine_cc_z']
varnames = ['blind:cosine_cc_z', 'sighted:cosine_cc_z']
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
figsize=[9, .6 + len(varnames) * .3],
var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);
display(az.summary(trace, hdi_prob=.95, var_names=varnames))
| mean | sd | hdi_2.5% | hdi_97.5% | mcse_mean | mcse_sd | ess_bulk | ess_tail | r_hat | |
|---|---|---|---|---|---|---|---|---|---|
| blind:cosine_cc_z | 0.123 | 0.065 | -0.002 | 0.250 | 0.002 | 0.001 | 1807.0 | 2726.0 | 1.0 |
| sighted:cosine_cc_z | 0.388 | 0.031 | 0.330 | 0.451 | 0.000 | 0.000 | 4533.0 | 3332.0 | 1.0 |
m_subs = bambi.Model('rating_z ~ 1'
+ ' + group_eff*frequency_z'
+ ' + group_eff*concreteness_z'
+ ' + group_eff*cosine_subs_z'
+ ' + group_eff*swow_all_z'
+ ' + (1 + frequency_z + concreteness_z + cosine_subs_z + swow_all_z|pp_id)'
+ ' + (1 + group_eff|dimension)'
+ ' + (1 + group_eff|color)',
df_joint[(df_joint['experiment'] != 'replication_2') & (df_joint['self_vs_other'] == 'self')]
)
r_subs = m_subs.fit(
init='advi+adapt_diag',
chains=4,
draws=1000,
tune=1000,
n_init=10000,
target_accept=.95,
)
Auto-assigning NUTS sampler... [INFO] Auto-assigning NUTS sampler... Initializing NUTS using advi+adapt_diag... [INFO] Initializing NUTS using advi+adapt_diag...
Finished [100%]: Average Loss = 16,632 [INFO] Finished [100%]: Average Loss = 16,632 Multiprocess sampling (4 chains in 4 jobs) [INFO] Multiprocess sampling (4 chains in 4 jobs) NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_subs_z, group_eff:cosine_subs_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_subs_z|pp_id_sigma, cosine_subs_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma] [INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_subs_z, group_eff:cosine_subs_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_subs_z|pp_id_sigma, cosine_subs_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 357 seconds. [INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 357 seconds.
# compute and plot conditional effect of cosine in sighted and blind groups
trace_subs = deepcopy(r_subs.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_subs_z'] = trace_subs['cosine_subs_z'] - trace_subs['group_eff:cosine_subs_z']
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_subs_z'] = trace_subs['cosine_subs_z'] + trace_subs['group_eff:cosine_subs_z']
varnames = [
'blind:cosine_cc_z', 'sighted:cosine_cc_z',
'blind:cosine_subs_z', 'sighted:cosine_subs_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
figsize=[9, .6 + len(varnames) * .3],
var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);
display(az.summary(trace, hdi_prob=.95, var_names=varnames))
| mean | sd | hdi_2.5% | hdi_97.5% | mcse_mean | mcse_sd | ess_bulk | ess_tail | r_hat | |
|---|---|---|---|---|---|---|---|---|---|
| blind:cosine_cc_z | 0.123 | 0.065 | -0.002 | 0.250 | 0.002 | 0.001 | 1807.0 | 2726.0 | 1.0 |
| sighted:cosine_cc_z | 0.388 | 0.031 | 0.330 | 0.451 | 0.000 | 0.000 | 4533.0 | 3332.0 | 1.0 |
| blind:cosine_subs_z | 0.225 | 0.047 | 0.129 | 0.312 | 0.001 | 0.001 | 2332.0 | 2901.0 | 1.0 |
| sighted:cosine_subs_z | 0.446 | 0.025 | 0.396 | 0.493 | 0.000 | 0.000 | 5835.0 | 2787.0 | 1.0 |
m_fic = bambi.Model('rating_z ~ 1'
+ ' + group_eff*frequency_z'
+ ' + group_eff*concreteness_z'
+ ' + group_eff*cosine_fic_z'
+ ' + group_eff*swow_all_z'
+ ' + (1 + frequency_z + concreteness_z + cosine_fic_z + swow_all_z|pp_id)'
+ ' + (1 + group_eff|dimension)'
+ ' + (1 + group_eff|color)',
df_joint[(df_joint['experiment'] != 'replication_2') & (df_joint['self_vs_other'] == 'self')]
)
r_fic = m_fic.fit(
init='advi+adapt_diag',
chains=4,
draws=1000,
tune=1000,
n_init=10000,
target_accept=.95,
)
Auto-assigning NUTS sampler... [INFO] Auto-assigning NUTS sampler... Initializing NUTS using advi+adapt_diag... [INFO] Initializing NUTS using advi+adapt_diag...
Finished [100%]: Average Loss = 16,671 [INFO] Finished [100%]: Average Loss = 16,671 Multiprocess sampling (4 chains in 4 jobs) [INFO] Multiprocess sampling (4 chains in 4 jobs) NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_z, group_eff:cosine_fic_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_z|pp_id_sigma, cosine_fic_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma] [INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_fic_z, group_eff:cosine_fic_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_fic_z|pp_id_sigma, cosine_fic_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 362 seconds. [INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 362 seconds.
# compute and plot conditional effect of cosine in sighted and blind groups
trace_fic = deepcopy(r_fic.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_fic_z'] = trace_fic['cosine_fic_z'] - trace_fic['group_eff:cosine_fic_z']
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_fic_z'] = trace_fic['cosine_fic_z'] + trace_fic['group_eff:cosine_fic_z']
varnames = [
'blind:cosine_cc_z', 'sighted:cosine_cc_z',
'blind:cosine_subs_z', 'sighted:cosine_subs_z',
'blind:cosine_fic_z', 'sighted:cosine_fic_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
figsize=[9, .6 + len(varnames) * .3],
var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);
display(az.summary(trace, hdi_prob=.95, var_names=varnames))
| mean | sd | hdi_2.5% | hdi_97.5% | mcse_mean | mcse_sd | ess_bulk | ess_tail | r_hat | |
|---|---|---|---|---|---|---|---|---|---|
| blind:cosine_cc_z | 0.123 | 0.065 | -0.002 | 0.250 | 0.002 | 0.001 | 1807.0 | 2726.0 | 1.0 |
| sighted:cosine_cc_z | 0.388 | 0.031 | 0.330 | 0.451 | 0.000 | 0.000 | 4533.0 | 3332.0 | 1.0 |
| blind:cosine_subs_z | 0.225 | 0.047 | 0.129 | 0.312 | 0.001 | 0.001 | 2332.0 | 2901.0 | 1.0 |
| sighted:cosine_subs_z | 0.446 | 0.025 | 0.396 | 0.493 | 0.000 | 0.000 | 5835.0 | 2787.0 | 1.0 |
| blind:cosine_fic_z | 0.379 | 0.047 | 0.284 | 0.465 | 0.001 | 0.001 | 2140.0 | 2644.0 | 1.0 |
| sighted:cosine_fic_z | 0.520 | 0.026 | 0.472 | 0.572 | 0.000 | 0.000 | 7133.0 | 3144.0 | 1.0 |
m_spok = bambi.Model('rating_z ~ 1'
+ ' + group_eff*frequency_z'
+ ' + group_eff*concreteness_z'
+ ' + group_eff*cosine_spok_z'
+ ' + group_eff*swow_all_z'
+ ' + (1 + frequency_z + concreteness_z + cosine_spok_z + swow_all_z|pp_id)'
+ ' + (1 + group_eff|dimension)'
+ ' + (1 + group_eff|color)',
df_joint[(df_joint['experiment'] != 'replication_2') & (df_joint['self_vs_other'] == 'self')]
)
r_spok = m_spok.fit(
init='advi+adapt_diag',
chains=4,
draws=1000,
tune=1000,
n_init=10000,
target_accept=.95,
)
Auto-assigning NUTS sampler... [INFO] Auto-assigning NUTS sampler... Initializing NUTS using advi+adapt_diag... [INFO] Initializing NUTS using advi+adapt_diag...
Finished [100%]: Average Loss = 16,714 [INFO] Finished [100%]: Average Loss = 16,714 Multiprocess sampling (4 chains in 4 jobs) [INFO] Multiprocess sampling (4 chains in 4 jobs) NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_spok_z, group_eff:cosine_spok_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_spok_z|pp_id_sigma, cosine_spok_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma] [INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_spok_z, group_eff:cosine_spok_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_spok_z|pp_id_sigma, cosine_spok_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 362 seconds. [INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 362 seconds.
# compute and plot conditional effect of cosine in sighted and blind groups
trace_spok = deepcopy(r_spok.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_spok_z'] = trace_spok['cosine_spok_z'] - trace_spok['group_eff:cosine_spok_z']
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_spok_z'] = trace_spok['cosine_spok_z'] + trace_spok['group_eff:cosine_spok_z']
varnames = [
'blind:cosine_cc_z', 'sighted:cosine_cc_z',
'blind:cosine_subs_z', 'sighted:cosine_subs_z',
'blind:cosine_fic_z', 'sighted:cosine_fic_z',
'blind:cosine_spok_z', 'sighted:cosine_spok_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
figsize=[9, .6 + len(varnames) * .3],
var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);
display(az.summary(trace, hdi_prob=.95, var_names=varnames))
| mean | sd | hdi_2.5% | hdi_97.5% | mcse_mean | mcse_sd | ess_bulk | ess_tail | r_hat | |
|---|---|---|---|---|---|---|---|---|---|
| blind:cosine_cc_z | 0.123 | 0.065 | -0.002 | 0.250 | 0.002 | 0.001 | 1807.0 | 2726.0 | 1.0 |
| sighted:cosine_cc_z | 0.388 | 0.031 | 0.330 | 0.451 | 0.000 | 0.000 | 4533.0 | 3332.0 | 1.0 |
| blind:cosine_subs_z | 0.225 | 0.047 | 0.129 | 0.312 | 0.001 | 0.001 | 2332.0 | 2901.0 | 1.0 |
| sighted:cosine_subs_z | 0.446 | 0.025 | 0.396 | 0.493 | 0.000 | 0.000 | 5835.0 | 2787.0 | 1.0 |
| blind:cosine_fic_z | 0.379 | 0.047 | 0.284 | 0.465 | 0.001 | 0.001 | 2140.0 | 2644.0 | 1.0 |
| sighted:cosine_fic_z | 0.520 | 0.026 | 0.472 | 0.572 | 0.000 | 0.000 | 7133.0 | 3144.0 | 1.0 |
| blind:cosine_spok_z | 0.191 | 0.045 | 0.108 | 0.283 | 0.001 | 0.001 | 2947.0 | 3054.0 | 1.0 |
| sighted:cosine_spok_z | 0.283 | 0.025 | 0.235 | 0.334 | 0.000 | 0.000 | 6465.0 | 3264.0 | 1.0 |
m_acad = bambi.Model('rating_z ~ 1'
+ ' + group_eff*frequency_z'
+ ' + group_eff*concreteness_z'
+ ' + group_eff*cosine_acad_z'
+ ' + group_eff*swow_all_z'
+ ' + (1 + frequency_z + concreteness_z + cosine_acad_z + swow_all_z|pp_id)'
+ ' + (1 + group_eff|dimension)'
+ ' + (1 + group_eff|color)',
df_joint[(df_joint['experiment'] != 'replication_2') & (df_joint['self_vs_other'] == 'self')]
)
r_acad = m_acad.fit(
init='advi+adapt_diag',
chains=4,
draws=1000,
tune=1000,
n_init=10000,
target_accept=.95,
)
Auto-assigning NUTS sampler... [INFO] Auto-assigning NUTS sampler... Initializing NUTS using advi+adapt_diag... [INFO] Initializing NUTS using advi+adapt_diag...
Finished [100%]: Average Loss = 16,673 [INFO] Finished [100%]: Average Loss = 16,673 Multiprocess sampling (4 chains in 4 jobs) [INFO] Multiprocess sampling (4 chains in 4 jobs) NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_acad_z, group_eff:cosine_acad_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_acad_z|pp_id_sigma, cosine_acad_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma] [INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_acad_z, group_eff:cosine_acad_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_acad_z|pp_id_sigma, cosine_acad_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 372 seconds. [INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 372 seconds.
# compute and plot conditional effect of cosine in sighted and blind groups
trace_acad = deepcopy(r_acad.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_acad_z'] = trace_acad['cosine_acad_z'] - trace_acad['group_eff:cosine_acad_z']
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_acad_z'] = trace_acad['cosine_acad_z'] + trace_acad['group_eff:cosine_acad_z']
varnames = [
'blind:cosine_cc_z', 'sighted:cosine_cc_z',
'blind:cosine_subs_z', 'sighted:cosine_subs_z',
'blind:cosine_fic_z', 'sighted:cosine_fic_z',
'blind:cosine_spok_z', 'sighted:cosine_spok_z',
'blind:cosine_acad_z', 'sighted:cosine_acad_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
figsize=[9, .6 + len(varnames) * .3],
var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);
display(az.summary(trace, hdi_prob=.95, var_names=varnames))
| mean | sd | hdi_2.5% | hdi_97.5% | mcse_mean | mcse_sd | ess_bulk | ess_tail | r_hat | |
|---|---|---|---|---|---|---|---|---|---|
| blind:cosine_cc_z | 0.123 | 0.065 | -0.002 | 0.250 | 0.002 | 0.001 | 1807.0 | 2726.0 | 1.0 |
| sighted:cosine_cc_z | 0.388 | 0.031 | 0.330 | 0.451 | 0.000 | 0.000 | 4533.0 | 3332.0 | 1.0 |
| blind:cosine_subs_z | 0.225 | 0.047 | 0.129 | 0.312 | 0.001 | 0.001 | 2332.0 | 2901.0 | 1.0 |
| sighted:cosine_subs_z | 0.446 | 0.025 | 0.396 | 0.493 | 0.000 | 0.000 | 5835.0 | 2787.0 | 1.0 |
| blind:cosine_fic_z | 0.379 | 0.047 | 0.284 | 0.465 | 0.001 | 0.001 | 2140.0 | 2644.0 | 1.0 |
| sighted:cosine_fic_z | 0.520 | 0.026 | 0.472 | 0.572 | 0.000 | 0.000 | 7133.0 | 3144.0 | 1.0 |
| blind:cosine_spok_z | 0.191 | 0.045 | 0.108 | 0.283 | 0.001 | 0.001 | 2947.0 | 3054.0 | 1.0 |
| sighted:cosine_spok_z | 0.283 | 0.025 | 0.235 | 0.334 | 0.000 | 0.000 | 6465.0 | 3264.0 | 1.0 |
| blind:cosine_acad_z | -0.008 | 0.037 | -0.081 | 0.066 | 0.001 | 0.001 | 2731.0 | 3069.0 | 1.0 |
| sighted:cosine_acad_z | 0.083 | 0.022 | 0.039 | 0.124 | 0.000 | 0.000 | 5034.0 | 3255.0 | 1.0 |
m_mag = bambi.Model('rating_z ~ 1'
+ ' + group_eff*frequency_z'
+ ' + group_eff*concreteness_z'
+ ' + group_eff*cosine_mag_z'
+ ' + group_eff*swow_all_z'
+ ' + (1 + frequency_z + concreteness_z + cosine_mag_z + swow_all_z|pp_id)'
+ ' + (1 + group_eff|dimension)'
+ ' + (1 + group_eff|color)',
df_joint[(df_joint['experiment'] != 'replication_2') & (df_joint['self_vs_other'] == 'self')]
)
r_mag = m_mag.fit(
init='advi+adapt_diag',
chains=4,
draws=1000,
tune=1000,
n_init=10000,
target_accept=.95,
)
Auto-assigning NUTS sampler... [INFO] Auto-assigning NUTS sampler... Initializing NUTS using advi+adapt_diag... [INFO] Initializing NUTS using advi+adapt_diag...
Finished [100%]: Average Loss = 16,688 [INFO] Finished [100%]: Average Loss = 16,688 Multiprocess sampling (4 chains in 4 jobs) [INFO] Multiprocess sampling (4 chains in 4 jobs) NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_mag_z, group_eff:cosine_mag_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_mag_z|pp_id_sigma, cosine_mag_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma] [INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_mag_z, group_eff:cosine_mag_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_mag_z|pp_id_sigma, cosine_mag_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 372 seconds. [INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 372 seconds. There was 1 divergence after tuning. Increase `target_accept` or reparameterize. [ERROR] There was 1 divergence after tuning. Increase `target_accept` or reparameterize.
# compute and plot conditional effect of cosine in sighted and blind groups
trace_mag = deepcopy(r_mag.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_mag_z'] = trace_mag['cosine_mag_z'] - trace_mag['group_eff:cosine_mag_z']
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_mag_z'] = trace_mag['cosine_mag_z'] + trace_mag['group_eff:cosine_mag_z']
varnames = [
'blind:cosine_cc_z', 'sighted:cosine_cc_z',
'blind:cosine_subs_z', 'sighted:cosine_subs_z',
'blind:cosine_fic_z', 'sighted:cosine_fic_z',
'blind:cosine_spok_z', 'sighted:cosine_spok_z',
'blind:cosine_acad_z', 'sighted:cosine_acad_z',
'blind:cosine_mag_z', 'sighted:cosine_mag_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
figsize=[9, .6 + len(varnames) * .3],
var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);
display(az.summary(trace, hdi_prob=.95, var_names=varnames))
| mean | sd | hdi_2.5% | hdi_97.5% | mcse_mean | mcse_sd | ess_bulk | ess_tail | r_hat | |
|---|---|---|---|---|---|---|---|---|---|
| blind:cosine_cc_z | 0.123 | 0.065 | -0.002 | 0.250 | 0.002 | 0.001 | 1807.0 | 2726.0 | 1.0 |
| sighted:cosine_cc_z | 0.388 | 0.031 | 0.330 | 0.451 | 0.000 | 0.000 | 4533.0 | 3332.0 | 1.0 |
| blind:cosine_subs_z | 0.225 | 0.047 | 0.129 | 0.312 | 0.001 | 0.001 | 2332.0 | 2901.0 | 1.0 |
| sighted:cosine_subs_z | 0.446 | 0.025 | 0.396 | 0.493 | 0.000 | 0.000 | 5835.0 | 2787.0 | 1.0 |
| blind:cosine_fic_z | 0.379 | 0.047 | 0.284 | 0.465 | 0.001 | 0.001 | 2140.0 | 2644.0 | 1.0 |
| sighted:cosine_fic_z | 0.520 | 0.026 | 0.472 | 0.572 | 0.000 | 0.000 | 7133.0 | 3144.0 | 1.0 |
| blind:cosine_spok_z | 0.191 | 0.045 | 0.108 | 0.283 | 0.001 | 0.001 | 2947.0 | 3054.0 | 1.0 |
| sighted:cosine_spok_z | 0.283 | 0.025 | 0.235 | 0.334 | 0.000 | 0.000 | 6465.0 | 3264.0 | 1.0 |
| blind:cosine_acad_z | -0.008 | 0.037 | -0.081 | 0.066 | 0.001 | 0.001 | 2731.0 | 3069.0 | 1.0 |
| sighted:cosine_acad_z | 0.083 | 0.022 | 0.039 | 0.124 | 0.000 | 0.000 | 5034.0 | 3255.0 | 1.0 |
| blind:cosine_mag_z | 0.119 | 0.047 | 0.021 | 0.207 | 0.001 | 0.001 | 2077.0 | 2428.0 | 1.0 |
| sighted:cosine_mag_z | 0.297 | 0.024 | 0.251 | 0.346 | 0.000 | 0.000 | 6631.0 | 3095.0 | 1.0 |
m_news = bambi.Model('rating_z ~ 1'
+ ' + group_eff*frequency_z'
+ ' + group_eff*concreteness_z'
+ ' + group_eff*cosine_news_z'
+ ' + group_eff*swow_all_z'
+ ' + (1 + frequency_z + concreteness_z + cosine_news_z + swow_all_z|pp_id)'
+ ' + (1 + group_eff|dimension)'
+ ' + (1 + group_eff|color)',
df_joint[(df_joint['experiment'] != 'replication_2') & (df_joint['self_vs_other'] == 'self')]
)
r_news = m_news.fit(
init='advi+adapt_diag',
chains=4,
draws=1000,
tune=1000,
n_init=10000,
target_accept=.95,
)
Auto-assigning NUTS sampler... [INFO] Auto-assigning NUTS sampler... Initializing NUTS using advi+adapt_diag... [INFO] Initializing NUTS using advi+adapt_diag...
Finished [100%]: Average Loss = 16,607 [INFO] Finished [100%]: Average Loss = 16,607 Multiprocess sampling (4 chains in 4 jobs) [INFO] Multiprocess sampling (4 chains in 4 jobs) NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_news_z, group_eff:cosine_news_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_news_z|pp_id_sigma, cosine_news_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma] [INFO] NUTS: [Intercept, group_eff, frequency_z, group_eff:frequency_z, concreteness_z, group_eff:concreteness_z, cosine_news_z, group_eff:cosine_news_z, swow_all_z, group_eff:swow_all_z, 1|pp_id_sigma, 1|pp_id_offset, frequency_z|pp_id_sigma, frequency_z|pp_id_offset, concreteness_z|pp_id_sigma, concreteness_z|pp_id_offset, cosine_news_z|pp_id_sigma, cosine_news_z|pp_id_offset, swow_all_z|pp_id_sigma, swow_all_z|pp_id_offset, 1|dimension_sigma, 1|dimension_offset, group_eff|dimension_sigma, group_eff|dimension_offset, 1|color_sigma, 1|color_offset, group_eff|color_sigma, group_eff|color_offset, rating_z_sigma]
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 363 seconds. [INFO] Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 363 seconds.
# compute and plot conditional effect of cosine in sighted and blind groups
trace_news = deepcopy(r_news.posterior)
# effect of cosine in blind group in orginal experiment
trace['blind:cosine_news_z'] = trace_news['cosine_news_z'] - trace_news['group_eff:cosine_news_z']
# effect of cosine in sighted group across both experiments
trace['sighted:cosine_news_z'] = trace_news['cosine_news_z'] + trace_news['group_eff:cosine_news_z']
varnames = [
'blind:cosine_cc_z', 'sighted:cosine_cc_z',
'blind:cosine_subs_z', 'sighted:cosine_subs_z',
'blind:cosine_fic_z', 'sighted:cosine_fic_z',
'blind:cosine_spok_z', 'sighted:cosine_spok_z',
'blind:cosine_acad_z', 'sighted:cosine_acad_z',
'blind:cosine_mag_z', 'sighted:cosine_mag_z',
'blind:cosine_news_z', 'sighted:cosine_news_z',
]
g = az.plot_forest(trace, combined=True, hdi_prob=.95,
figsize=[9, .6 + len(varnames) * .3],
var_names=varnames)
g[0].axvline(0, color='.8', linewidth=2);
display(az.summary(trace, hdi_prob=.95, var_names=varnames))
| mean | sd | hdi_2.5% | hdi_97.5% | mcse_mean | mcse_sd | ess_bulk | ess_tail | r_hat | |
|---|---|---|---|---|---|---|---|---|---|
| blind:cosine_cc_z | 0.123 | 0.065 | -0.002 | 0.250 | 0.002 | 0.001 | 1807.0 | 2726.0 | 1.0 |
| sighted:cosine_cc_z | 0.388 | 0.031 | 0.330 | 0.451 | 0.000 | 0.000 | 4533.0 | 3332.0 | 1.0 |
| blind:cosine_subs_z | 0.225 | 0.047 | 0.129 | 0.312 | 0.001 | 0.001 | 2332.0 | 2901.0 | 1.0 |
| sighted:cosine_subs_z | 0.446 | 0.025 | 0.396 | 0.493 | 0.000 | 0.000 | 5835.0 | 2787.0 | 1.0 |
| blind:cosine_fic_z | 0.379 | 0.047 | 0.284 | 0.465 | 0.001 | 0.001 | 2140.0 | 2644.0 | 1.0 |
| sighted:cosine_fic_z | 0.520 | 0.026 | 0.472 | 0.572 | 0.000 | 0.000 | 7133.0 | 3144.0 | 1.0 |
| blind:cosine_spok_z | 0.191 | 0.045 | 0.108 | 0.283 | 0.001 | 0.001 | 2947.0 | 3054.0 | 1.0 |
| sighted:cosine_spok_z | 0.283 | 0.025 | 0.235 | 0.334 | 0.000 | 0.000 | 6465.0 | 3264.0 | 1.0 |
| blind:cosine_acad_z | -0.008 | 0.037 | -0.081 | 0.066 | 0.001 | 0.001 | 2731.0 | 3069.0 | 1.0 |
| sighted:cosine_acad_z | 0.083 | 0.022 | 0.039 | 0.124 | 0.000 | 0.000 | 5034.0 | 3255.0 | 1.0 |
| blind:cosine_mag_z | 0.119 | 0.047 | 0.021 | 0.207 | 0.001 | 0.001 | 2077.0 | 2428.0 | 1.0 |
| sighted:cosine_mag_z | 0.297 | 0.024 | 0.251 | 0.346 | 0.000 | 0.000 | 6631.0 | 3095.0 | 1.0 |
| blind:cosine_news_z | 0.008 | 0.036 | -0.060 | 0.081 | 0.001 | 0.001 | 2067.0 | 2876.0 | 1.0 |
| sighted:cosine_news_z | 0.122 | 0.019 | 0.082 | 0.157 | 0.000 | 0.000 | 6555.0 | 3590.0 | 1.0 |
varnames = [
'sighted:cosine_cc_z',
'sighted:cosine_subs_z',
'sighted:cosine_fic_z',
'sighted:cosine_spok_z',
'sighted:cosine_acad_z',
'sighted:cosine_mag_z',
'sighted:cosine_news_z',
'blind:cosine_cc_z',
'blind:cosine_subs_z',
'blind:cosine_fic_z',
'blind:cosine_spok_z',
'blind:cosine_acad_z',
'blind:cosine_mag_z',
'blind:cosine_news_z',
]
trace_df = az.summary(trace, hdi_prob=.95, var_names=varnames).reset_index()
sns.set(palette='colorblind', style='whitegrid')
trace_df['group'] = trace_df['index'].apply(lambda x: x.split(':')[0])
trace_df['predictor'] = trace_df['index'].apply(lambda x: x.split(':')[1])
g, ax = plt.subplots(figsize=[3.2, 3.2])
ax.axvline(0, color='.8', linewidth=2)
order = [
'cosine_acad_z',
'cosine_news_z',
'cosine_spok_z',
'cosine_mag_z',
'cosine_cc_z',
'cosine_subs_z',
'cosine_fic_z',
]
sns.pointplot(data=trace_df, hue='group', x='mean', y='predictor', markers=['^', 'o'], join=False, ax=ax, order=order,
palette=sns.color_palette()[0:], dodge=.2)
hdi_df = trace_df.melt(id_vars=['predictor', 'group'], value_vars=['hdi_2.5%', 'hdi_97.5%'])
sns.pointplot(data=hdi_df, hue='group', markers='', x='value', order=order,
y='predictor', ax=ax, join=False,
palette=sns.color_palette()[0:], dodge=.2)
ax.set(xlim=[-.1, .6], xticks=[-.1, 0, .1, .2, .3, .4, .5, .6],
ylabel='', xlabel='effect size (standardized coefficient)',
title='95% CIs for embedding projections\nfrom various corpora')
ax.set(yticklabels=[
'COCA-academic projection',
'COCA-news projection',
'COCA-spoken projection',
'COCA-magazine projection',
'Common Crawl projection',
'OpenSubtitles projection',
'COCA-fiction projection',
])
labels = ax.get_legend_handles_labels()
ax.legend(handles=labels[0][:2], labels=labels[1][:2],
bbox_to_anchor=(1, 1), loc=2, borderaxespad=0, frameon=False)
plt.savefig('figures/corpus_variation_forest.pdf', bbox_inches='tight')
/opt/homebrew/lib/python3.9/site-packages/seaborn/categorical.py:1727: UserWarning: You passed a edgecolor/edgecolors ((0.00392156862745098, 0.45098039215686275, 0.6980392156862745)) for an unfilled marker (''). Matplotlib is ignoring the edgecolor in favor of the facecolor. This behavior may change in the future.
ax.scatter(x, y, label=hue_level,
/opt/homebrew/lib/python3.9/site-packages/seaborn/categorical.py:1727: UserWarning: You passed a edgecolor/edgecolors ((0.8705882352941177, 0.5607843137254902, 0.0196078431372549)) for an unfilled marker (''). Matplotlib is ignoring the edgecolor in favor of the facecolor. This behavior may change in the future.
ax.scatter(x, y, label=hue_level,
Instead of using conditional effect sizes from the models as a comparison, we can also compare the models on their out-of-sample predictive accuracy. Essentially we're looking to see which predictor, if included, makes the model worst.
Using prediction/cross-validation for model comparison has distinct advantages in some situations, but in our case (when we're not varying model complexity or structure, but only replacing a single predictor) the results will probably match our inferences from the conditional effect size plots.
display(az.compare({
'COCA fiction': r_fic,
'COCA spoken': r_spok,
'COCA academic': r_acad,
'COCA magazine': r_mag,
'COCA news': r_news,
'Common Crawl': r_cc,
'OpenSubtitles': r_subs,
}).round(2))
/opt/homebrew/lib/python3.9/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations. warnings.warn( /opt/homebrew/lib/python3.9/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations. warnings.warn( /opt/homebrew/lib/python3.9/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations. warnings.warn( /opt/homebrew/lib/python3.9/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations. warnings.warn( /opt/homebrew/lib/python3.9/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations. warnings.warn( /opt/homebrew/lib/python3.9/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations. warnings.warn( /opt/homebrew/lib/python3.9/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations. warnings.warn(
| rank | elpd_loo | p_loo | elpd_diff | weight | se | dse | warning | scale | |
|---|---|---|---|---|---|---|---|---|---|
| COCA fiction | 0 | -13453.41 | 161.51 | 0.00 | 0.62 | 65.20 | 0.00 | True | log |
| OpenSubtitles | 1 | -13506.96 | 163.30 | 53.55 | 0.38 | 65.09 | 21.85 | True | log |
| Common Crawl | 2 | -13607.46 | 160.27 | 154.05 | 0.00 | 64.68 | 22.34 | True | log |
| COCA magazine | 3 | -13617.69 | 156.11 | 164.28 | 0.00 | 64.70 | 20.72 | True | log |
| COCA spoken | 4 | -13635.77 | 155.96 | 182.36 | 0.00 | 64.20 | 22.48 | True | log |
| COCA news | 5 | -13688.29 | 152.67 | 234.88 | 0.00 | 64.27 | 22.24 | True | log |
| COCA academic | 6 | -13703.46 | 152.80 | 250.04 | 0.00 | 63.97 | 21.73 | True | log |
As expected, the model with COCA-fiction performs best, although the subtitle model is a close second. These models have in common that they contain many well-formed sentences of a decent length, which contain references to color in both literal and metaphorical sense.
The comparison algorithm does warn that the shape parameter of the pareto distribution is too large for some observations. This is common with hierarchical models and shouldn't be a problem if it concerns only a few observations. We can check this by inspecting the LOO-statistics more closely.
az.loo(r_fic)
/opt/homebrew/lib/python3.9/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations. warnings.warn(
Computed from 4000 posterior samples and 9417 observations log-likelihood matrix.
Estimate SE
elpd_loo -13453.41 65.20
p_loo 161.51 -
There has been a warning during the calculation. Please check the results.
------
Pareto k diagnostic values:
Count Pct.
(-Inf, 0.5] (good) 9399 99.8%
(0.5, 0.7] (ok) 15 0.2%
(0.7, 1] (bad) 3 0.0%
(1, Inf) (very bad) 0 0.0%
It appears that for the COCA-fiction model, for instance, there are only 3 observations in the "bad" range. This is not overly problematic given the nearly 10,000 observations that are in the correct range.
R-hat and other Markov chain diagnostics looked good, but it's still worth doing a few quick visual model checks.
We want all the Markov chains for a single variable to look lined up in the density plot on the left, but nice and fuzzy (i.e. not autocorrelated) on the right.
g = az.plot_trace(r_cc, var_names=['Intercept', 'group_eff', 'cosine_cc_z', 'group_eff:cosine_cc_z'])
plt.tight_layout()
g = az.plot_trace(r_subs, var_names=['Intercept', 'group_eff', 'cosine_subs_z', 'group_eff:cosine_subs_z'])
plt.tight_layout()
g = az.plot_trace(r_fic, var_names=['Intercept', 'group_eff', 'cosine_fic_z', 'group_eff:cosine_fic_z'])
plt.tight_layout()
g = az.plot_trace(r_spok, var_names=['Intercept', 'group_eff', 'cosine_spok_z', 'group_eff:cosine_spok_z'])
plt.tight_layout()
g = az.plot_trace(r_acad, var_names=['Intercept', 'group_eff', 'cosine_acad_z', 'group_eff:cosine_acad_z'])
plt.tight_layout()
g = az.plot_trace(r_mag, var_names=['Intercept', 'group_eff', 'cosine_mag_z', 'group_eff:cosine_mag_z'])
plt.tight_layout()
g = az.plot_trace(r_news, var_names=['Intercept', 'group_eff', 'cosine_news_z', 'group_eff:cosine_news_z'])
plt.tight_layout()
Check if the model's predictions line up with the predictions in our observed data (i.e. there are no weird biases etc.)
m_cc.predict(r_cc, kind='pps')
g = az.plot_ppc(r_cc, kind='cumulative')
m_subs.predict(r_subs, kind='pps')
g = az.plot_ppc(r_subs, kind='cumulative')
m_fic.predict(r_fic, kind='pps')
g = az.plot_ppc(r_fic, kind='cumulative')
m_spok.predict(r_spok, kind='pps')
g = az.plot_ppc(r_spok, kind='cumulative')
m_acad.predict(r_acad, kind='pps')
g = az.plot_ppc(r_acad, kind='cumulative')
m_mag.predict(r_mag, kind='pps')
g = az.plot_ppc(r_mag, kind='cumulative')
m_news.predict(r_news, kind='pps')
g = az.plot_ppc(r_news, kind='cumulative')
convert_notebook('experiment_2')